Francois Liot wrote:
>
> I observed a strange calculation answer, on both python 2.3.4 and 2.4.4
>
>> >> print 753343.44 - 753361.89
>
> -18.4500000001
>
>> >> print ( (753361.89*100) - (753343.44*100) ) / 100
>
> 18.45
>
> Can somebody help me to play correctly with decimal values?
A 64-bit binary floating point number can hold values between -1e308 and
+1e308, in only 64 bits of memory. Since 1e308 is a *lot* larger than
float(2**64) = ~1.8e19, it does this by splitting the number in a binary
fraction, and a multiplier (stored as an exponent).
Unfortunately, very few decimal fractions can be *exactly* represented
as binary fractions, so you often get representation errors:
http://docs.python.org/tut/node16.html
This is usually not much of a problem, since you usually end up rounding
things to a suitable number of decimals or significant digits when you
print them anyway (see below), but repr() doesn't do that -- it always
outputs enough digits to get back the *exact* binary representation if
you convert the string back to a floating point value again.
In practice, you can usually ignore this; just use the appropriate
output methods, and things will just work:
While pathological cases do exist, for most casual use of
floating-point arithmetic you'll see the result you expect
in the end if you simply round the display of your final
results to the number of decimal digits you expect. str()
usually suffices, and for finer control see the discussion
of Python's % format operator: the %g, %f and %e format codes
supply flexible and easy ways to round float results for
display.
(from the above link)
If you really need full control over this, no matter what, use the
Decimal type, as provided by the decimal module in the standard library.
See the library reference for the full story.
</F>
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